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If 5x=y+7, is (x−y)>0 ? [#permalink]
 05 Jun 2012, 20:27
Question Stats:
36% (02:11) correct
63% (00:53) wrong based on 38 sessions
If 5x=y+7, is (x−y)>0 ? (1) xy=6 (2) x and y are consecutive integers with the same sign
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Statement 1: xy=6 is not sufficient to answer the question because solving the equation gives y=3 when x is 2 and y is -10 when x is −3 5 .
5x=y+7
x=y+7 5 ................i
xy=6 ........................ ii
Replacing the value of x on eq ii: y(y+7) 5 =6
y 2 +7y=30
y 2 +10y−3y−30=0
y(y+10)−3(y+10)=0
(y+10)(y−3)=0
y=−10 or 3
If y=−10 , x=−3 5 . In this case, x−y=−3 5 −(−10)=47 5 . Yes.
If y=3 , x=2 . In this case, x−y=2−3=−1 . No.
In each case (x−y)>0 and <0 . Hence statement 1 is not sufficient.
Statement 2: If x and y are consecutive integers, x=2 and y=3 .
When x and y are consecutive integers, either x=y+1 or y=x+1 is possible.
(i) If x=y+1
5x=y+7
5(y+1)=y+7
4y=2
y=1 2 . Then x=3 2 . However this is not possible becase x and y are even not integers. So this option is not valid.
(ii) If y=x+1
5x=y+7
5x=x+1+7
4x=8
x=2
Then, y=3 . This is valid because x and y are consecutive integers.
So (x−y)=2−3=−1 . Hence statement 2 is sufficient.
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If 5x=y+7 , is (x−y)>0 ? Statement 1: xy=6 => 5x = (6/x) + 7 => 5x^2 - 7x - 6 =0 => (x-2)(5x+3)=0 => x = 2 or x= -3/5. So the solutions sets are (x,y) = (2,3) and (-3/5,-10). In case 1, x-y<0 and in case 2, x-y>0. Insufficient. Statement 2: x and y are consecutive integers with the same sign. Take x=k and y=k+1 => 5k = (k+1) + 7 => k=2. So one possible solution is x=2,y=3. Take y=k and x=k+1 => 5(k+1) = k + 7 => k = 1/2. So no solution possible in integers. Therefore x-y<0. Sufficient. The answer is B.
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Last edited by GyanOne on 06 Jun 2012, 17:44, edited 1 time in total.
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GyanOne wrote: => x = 2 or x= -3/5. So the solutions sets are (x,y) = (2,3) and (-3/5,-10). In both cases, x-y>0. Sufficient. isn't st-1 insufficient because of the above solution set? if (x,y) = (2,3), then x-y=2-3 = -1. a 'no' if (x,y) = (-3/5,-10), then x-y=-3/5+10= 47/5. a 'yes' so, insufficient.
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Re: If 5x=y+7, is (x−y)>0 ? [#permalink]
19 Feb 2013, 08:00
Bunuel, x and y are consecutive integers with the same signDoesn't the above indicate that y is bigger than x by 1?
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Re: If 5x=y+7, is (x−y)>0 ? [#permalink]
19 Feb 2013, 08:28
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Re: If 5x=y+7, is (x−y)>0 ? [#permalink]
19 Feb 2013, 08:55
Bunuel wrote: Sachin9 wrote: Bunuel,
x and y are consecutive integers with the same sign
Doesn't the above indicate that y is bigger than x by 1? No, it dose not. When we are told that x and y are consecutive integers, it doesn't necessarily mean that y=x+1 (y>x), it could be that x=y+1 (x>y). For example, check the following question: if-m-and-n-are-consecutive-positive-integers-is-m-greater-126287.html#p1031359Hope it helps. Bunuel, I checked The link you gave . There m has to be greater than n. But here in this question, it is given that x and y are consecutive. Meaning of consecutive from google indicates that y follows x.. con·sec·u·tive
/kənˈsekyətiv/
Adjective
Following continuously.
In unbroken or logical sequence.
Synonyms
successive - sequential - running - sequent - serialSo y has to be bigger than x right?
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Re: If 5x=y+7, is (x−y)>0 ? [#permalink]
19 Feb 2013, 08:59
Sachin9 wrote: Bunuel wrote: Sachin9 wrote: Bunuel,
x and y are consecutive integers with the same sign
Doesn't the above indicate that y is bigger than x by 1? No, it dose not. When we are told that x and y are consecutive integers, it doesn't necessarily mean that y=x+1 (y>x), it could be that x=y+1 (x>y). For example, check the following question: if-m-and-n-are-consecutive-positive-integers-is-m-greater-126287.html#p1031359Hope it helps. Bunuel, I checked The link you gave . There m has to be greater than n. But here in this question, it is given that x and y are consecutive. Meaning of consecutive from google indicates that y follows x.. con·sec·u·tive
/kənˈsekyətiv/
Adjective
Following continuously.
In unbroken or logical sequence.
Synonyms
successive - sequential - running - sequent - serialSo y has to be bigger than x right? Google is not conducting the test, GMAC does.
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Re: If 5x=y+7, is (x−y)>0 ? [#permalink]
19 Feb 2013, 09:44
lol 
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Re: If 5x=y+7, is (x−y)>0 ?
[#permalink]
19 Feb 2013, 09:44
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